1. Field of the Invention
This invention relates to a micro-machine. More particularly, the present invention relates to a movable micro-body having a movable plate.
2. Related Background Art
It is well known that, as a result of any attempt of downsizing a machine element, the surface force comes to take a large proportion relative to the body force in the total force exerted to the element. Therefore, it is a general practice to minimize the number of sliding parts and revolving parts when designing a micro-machine.
FIG. 16 of the accompanying drawings is a schematic perspective view of an optical deflector disclosed in U.S. Pat. No. 4,317,611, and FIG. 17 is an exploded perspective view of the optical deflector of FIG. 16, illustrating the internal structure thereof. FIGS. 18 and 19 are schematic cross sectional views of the silicon thin plate 1020 taken along lines 1003 and 1006 in FIG. 16, respectively.
A recess 1012 is formed in a substrate 1010 made of an insulating material. A pair of drive electrodes 1014, 1016 and a mirror support member 1032 are arranged on the bottom of the recess 1012. The silicon thin plate 1020 is formed integrally with a pair of torsion bars 1022, 1024 and a mirror 1030. The mirror 1030 is coated on the surface thereof with a substance showing a high optical reflectivity and supported by the torsion bars 1022, 1024 so as to be able to swing freely. The silicon thin plate 1020 is disposed opposite to the drive electrodes 1014, 1016 with a predetermined gap that reliably separates it from the electrodes.
The silicon thin plate 1020 is electrically grounded. As an alternating voltage is applied to the drive electrodes 1014, 1016, electrostatic attracting force is exerted onto the mirror 1030 to make the latter swing around the longitudinal axis of the torsion bars 1022, 1024.
The inventor of the present invention looked into the bearing rigidity of the mirror 1030. The bearing rigidity involves the torsional rigidity kθ of the torsion bars 1022, 1024 as observed around the longitudinal axis thereof and the deflection rigidities kx and ky as observed in the respective directions of x, y. The sense of torsion and the directions of x and y are shown in FIGS. 22A through 22C. The sense of torsion is indicated by means of the arrow in FIG. 22A, whereas the y and x directions are indicated respectively by means of the arrow in FIG. 22B and the arrow in FIG. 22C. The torsional rigidity refers to the torque necessary for twisting the torsion bars by a unit angle and the deflection rigidity refers to the force necessary for displacing the torsion bars in a direction perpendicular to the axis by a unit length. When the swinging body (movable body) is required to move in the swinging direction but not desired to move in the deflecting directions, it is desirable that the torsion bars show large deflection rigidities and a small torsional rigidity.
For the purpose of simplification, assume here that the cross section of the torsion bars taken along a direction perpendicular to the axis around which they are twisted shows a rectangle having long sides of a and short sides of b. The torsional rigidity kθ, the largest permissible angle of twist θmax and the deflection rigidities in the x and y directions kx and ky are expressed respectively by the formulas below;
                              k          θ                =                              2            ×                                          G                ⁢                                                                  ⁢                J                            l                                =                      2            ×                          β              ⁡                              (                                  a                  /                  b                                )                                      ⁢                                          G                ⁢                                                                  ⁢                a                ⁢                                                                  ⁢                                  b                  3                                            l                                                          (        1        )                                          θ          max                =                                            α              ⁡                              (                                  a                  /                  b                                )                                      ⁢            l            ⁢                                                  ⁢                          τ              max                                                          β              ⁡                              (                                  a                  /                  b                                )                                      ⁢            b            ⁢                                                  ⁢            G                                              (        2        )                                          k          x                =                              2            ×                                          192                ⁢                E                ⁢                                                                  ⁢                                  I                  x                                                            l                3                                              =                                    32              ⁢              E              ⁢                                                          ⁢                              a                3                            ⁢              b                                      l              3                                                          (        3        )                                                                                                                                                                                                                              k                            y                                                    =                                                                                    2                              ×                                                                                                192                                  ⁢                                  E                                  ⁢                                                                                                                                          ⁢                                                                      I                                    y                                                                                                                                    l                                  3                                                                                                                      =                                                                                          32                                ⁢                                E                                ⁢                                                                                                                                  ⁢                                a                                ⁢                                                                                                                                  ⁢                                                                  b                                  3                                                                                                                            l                                3                                                                                                                                                                                                                                                  J                          =                                                      β                            ⁢                                                                                                                  ⁢                            a                            ⁢                                                                                                                  ⁢                                                          b                              3                                                                                                                                                                                                                                                I                            x                                                    =                                                                                    a                              ⁢                                                                                                                          ⁢                                                              b                                3                                                                                      12                                                                                                                                                                                                                                      I                      y                                        =                                                                                            a                          3                                                ⁢                        b                                            12                                                                                                                                              a              >              b                                                          (        4        )            where    E: the transversal modulus of elasticity (Young's modulus) of the material of the torsion bars,    G: the longitudinal modulus of elasticity (Young's modulus) of the material of the torsion bars,    τmax: the strength of the material of the torsion bars,    a, b: the lengths of the sides of the rectangular cross section of the torsion bars,    l: the length of the torsion bars,    J: the secondary polar moment at the rectangular cross section of the torsion bars,    Ix: the secondary moment at the rectangular cross section of the torsion bars in the x direction and    Iy: the secondary moment at the rectangular cross section of the torsion bars in the y direction.
Note that α and β are coefficients as defined in Table 1 below.
TABLE 1a/b1.01.52.02.53.04.06.08.010.0∞α0.2080.2310.2460.2580.2670.2820.2990.3090.3130.333β0.1410.1960.2290.2490.2630.2810.2990.3090.3130.333α/β1.481.181.071.041.021.001.001.001.001.00
FIG. 20 of the accompanying drawings is a schematic illustration of a drive unit for driving a scanning mirror disclosed in Japanese Patent Application Laid-Open No. 6-82711. Referring to FIG. 20, the scanning mirror 3010 comprises a mirror face section 3012 formed typically by means of evaporation of aluminum on one of the oppositely disposed principal surfaces of a flat and rectangular glass plate 3011 and a rare earth type thin film permanent magnet 3013 formed typically by sputtering SmCo (samarium cobalt) on the other principal surface of the glass plate 3011. A pair of strip-shaped thin film torsion bars 3014 typically made of metal such as stainless steel or beryllium copper are rigidly secured to the respective middle points of the longitudinal opposite ends of the mirror face section 3012 at one of the opposite ends each thereof and to the unit main body (not shown) at the other end each. The scanning mirror 3010 is adapted to be angularly displaced to swing around the drive axis 3015 as the two torsion bars 3014 are twisted. The permanent magnet 3013 is magnetized in such a way that it shows opposite polarities at the opposite sides relative to the drive axis 3015.
Referring to FIG. 20, there is also shown a magnetism generating member 3020 formed by winding a coil 3021 around a coil frame 3022 and also around an axis that is perpendicular to the drive axis 3015 of the scanning mirror 3010 and disposed near the principal surface of the scanning mirror 3010 such that the permanent magnet 3013 is arranged with a predetermined distance separating the magnetism generating member from the principal surface.
The above arrangement is operated as the coil 3021 is electrically energized for excitation so as to generate magnetism having magnetic poles as shown in FIG. 21 from the magnetism generating member 3020. Then, attracting force and repelling force arise between the magnetic poles of the generated magnetism and those of the permanent magnet 3013 so that consequently the torsion bars 3014 of the scanning mirror 3010 are twisted. Thus, the scanning mirror 3010 can be angularly displaced around the drive axis 3015 in the sense as indicated by the arrows in FIG. 21 by a desired angle as a function of the magnetism generated from the magnetism generating member 3020.
However, the inventor of the present invention realized that the above described related art movable micro-bodies are accompanied by the following problems.
1. When the secondary polar moment J at the rectangular cross section of the torsion bars is reduced to raise the permissible angle of twist of the torsion bars of either of the above described movable micro-bodies, the deflection rigidity kx or ky of the torsion bars is also reduced to consequently make the movable micro-body liable to be affected by external vibrations.
2. When, on the other hand, the length l of the torsion bars is increased to raise the permissible angle of twist of the torsion bars, the deflection rigidity kx or ky of the torsion bars is reduced to consequently make the movable micro-body also liable to be affected by external vibrations.